Recently, owing to the development of various social medias, many social behaviors spread on multiple rather than a single social circles, which are naturally modeled as multilayer networks [1]}, [2]}, [3]}, [4]}. Similar to social reinforcement in one-layer network, there exists significant difference between exposure to multiple social circles (multilayer reinforcement) and multiple exposures to the same social circle (intra-layer reinforcement)[5]}. Specifically, individuals would be more convinced and have higher possibility for diffusion when receiving the same informative stimulus from different social circles. However, previous studies mainly concentrated on simple interactions between nodes and its replicas in different layers [6]}, [7]}, [8]}. The detailed impacts of multilayer reinforcement mechanism that engineers complex social contagion remain largely unknown.
